On 14 Aug 2012, at 20:55, Stephen P. King wrote:
On 8/14/2012 6:08 AM, Bruno Marchal wrote:
On 14 Aug 2012, at 07:26, Stephen P. King wrote:
On 8/13/2012 9:19 AM, Bruno Marchal wrote:
On 12 Aug 2012, at 20:05, Stephen P. King wrote:
<snip>
Does the measure cover an infinite or finite subset of the
universals?
[BM]
It covers the whole UD* (the entire execution of the UD, contained
in a tiny constructive part of arithmetical truth). It is infinite.
This follows easily from the first person indeterminacy invariance
(cf step seven).
Dear Bruno,
Please think about what I am writing here. My words might be
wrong, but please try to understand what I am saying.
I am.
OK, the UD* would span all of "time" (the partly ordered
sequence of events that are 1p content) is "implied" by that "tiny
constructable part" of arithmetically true statements (not truth!
Truth is not an object that is accessible nor should be considered
or inferred or implied to be). This makes the UD* an eternal process
that can be considered to by operating the combinators (or numbers
to state is crudely) over and over and over again in a concurrent
fashion. The 1p indeterminacy emerges from the span of this process,
the UD*. We cannot consistently argue that it is not available in
its entirety for any one piece of the UD for the purpose of
assigning truth valuations, unless we are going consider the medium
on which the UD is running is co-existent with the UD.
OK. The ontological primary medium is given by any universal system. I
have chosen arithmetic to fix the thing.
This is exactly why I argue that a physical world (that is a common
delusion of a mutually non-contradictory collection of 1p's) is and
must be considered to be on the same ontological plane as the
combinators.
That does not make any sense to me.
Since the physical worlds cannot be considered to be
ontologically primitive (since they require the UD*) then neither
can the combinators, as they have no distinguishably (or
availability for truth valuations), be considered to be
ontologically primitive.
If you don't have them, you can't build them. I will use the
abbreviation 'numbers for numbers OR combinators or Fortran program or
lambda terms or game of life pattern or ...
What I say is that without 'numbers, youwill never have 'numbers. We
cannot define 'numbers from less.
Both have to be considered as existing on the same ontological
level. Your proposition that we can have a consistent immaterial
basis for all existence is simply inconsistent and thus wrong.
You have to show the inconsistency.
Does the subset have to be representable as a Boolean algebra?
[BM]
This is ambiguous. I would say "yes" if by subset you mean the
initial segment of UD*.
We can only make a claim that the sentence that is making that
claim is true if and only if that subset can be identified in
contradistinction with the rest of the UD*. This is equivalent to
locating a single number within an infinite class of numbers. Given
that it is a fact that the integers have a measure of zero in
2^aleph_0,
There is no additive measure. If you are using a non additive measure,
then it depends on the choice of the measure, there are many. Anyway,
comp makes the measure problem bearing on infinite computations, some
including oracles, not the numbers.
then it follows that the initial segment of the UD* has a measure of
zero as well. A measure simply does not exist that would select the
correct segment and thus we cannot make that claim. It is only as
you wrote initially, "this is ambiguous". An ambiguous sentence is
not the same as a true (or false!) statement. My claim is that the
Boolean Representation criterion is true if and only if there exist
a physical implementation of the segment of the UD*.
Define physical implementation in your theory (or idea).
A physical state might be one that maximally exists
[BM]
... from the local first person points of view, of those dropping
the apple and trying to predict what they will feel. But there is
no physical state, only physical experience, which are not
definable in any third person point of view. A physical state, with
comp, is not an object.
There is no 3p unless there is a Boolean Representation
This not logically valid, although I agree, with the usual classical
comp.
and there cannot be a Boolean Representation without a collection of
mutually non-contradictory 1p observations.
Now, that is idealism. With comp that is true for the physical
reality, not for the arithmetical one, which we postulate.
The 1p indeterminacy must have "room" to put all of the copies out
first and then compared to each other (solving the NP-Complete
problem)
I just feel compassionate for your misleading obsession on NP.
and then and only then can we say that there is a true sentence.
Truth is not something that we can access without work. Work is a
physical action.
This is physicalism. I don't believe nor disbelieve it at the onset.
in universal numbers, but this does not really answer anything.
[BM]
Indeed, it is *the* problem, which comp formulate mathematically
(even arithmetically).
I am not the person that knows or even has the capacity to write
this up in a formal way, but I do understand it.
Then you have to succeed in explaining your point informally, but
sufficiently clearly so that some one with that capacity can work this
out.
Mathematical objects are not "symbols" in my mind, they are objects
that I can "feel".
Good.
This is the curse and the blessing of dyslexia.
The body problem is still open.
[BM]
But a big part is solved.
Yes, but what I am telling you is that all of it can be solved
by using Pratt's methodology!
I doubt this as it address only a small part of it, and does not take
the first indeterminacy into account, nor comp actually.
But the body problem vanishes if we follow Pratt's prescription!
[BM]
Explain how you derive F= ma in Pratt. I don't see any shadow of
this, nor even an awareness that to solve the body problem in that
setting. Pratt shows something interesting, not that the body
problem has vanished. Or write a paper showing this. None of the
ten problem on consciousness exposed in Michael Tye book are even
addressed, not to mention the body problem itself.
I understand your complaint, but you realize that you are saying
that because no one has written up a paper that you can read that
'shows a derivation of F=ma' that there is no solution.
Feynman derived it from the MW (to be short). And the MW is a
consequence of comp (to be short). Comp can explain F=ma, except that
it ca, still not explain the x and t in a = d^2x/dt^2. With comp, the
weird become obvious, and the obvious becomes hard, like the role of
the variable x and t. But that is the point.
By making physical events and abstract/mental/immaterial states
the Stone dual of each other, neither is primitive in the absolute
sense. They both emerge from the underlying primitive []<>.
[BM]
With which "[]<>"?
You know what I mean, my existence theory. Existence is that
which is necessarily possible, the sum of all that exists.
That does not help. Sorry.
You know what this is because you use it implicitly with your UD*
argument! All of the expressiong of the UD*, those aspects that it
represents must either exist on their own or be represented by other
things. Representations, such as numbers, can represent only
themselves only when they are physical patterns of physical stuff.
This makes hopeless the search for an explanation of the physical.
They are not free-floating meaningfulness.
Sure.
With comp, the universal arithmetical being already got the answer,
and answered it.
[]p = Bp & Dt
<>p = Dp V Bf
Do the p refer to something or are they empty symbols?
They refer to sigma_1 arithmetical proposition, or to computational
states occurring in UD*.
Bp = the sigma_1 complete arithmetical Beweisbar predicate (Gödel
1931)
Dp = ~B~p
Then we get for the sigma_1 p: []p -> p, p -> []<>p, and all we
need to show that p -> []<>p. It is just my incompetence which
provides us to know if this gives quantum mechanics or not. But the
theory is there. Comp gave no choice in this matter (pun included!).
I agree, but the very fact that there is a string of symbols
" []p -> p, p -> []<>p " and that string has a truthful meaning,
such that p -> []<>p, is because there is a physical world that
emerges from the computations that implement us.
You could have added: "and the only reason that there is a physical
world is a god that create it in 24 days".
Sorry but I don't buy that type of physical reality or God. That's gap
words for saying "we don't know". But with comp we already "know".
Let me illustrate the idea with a picture of an piece of art by MC
Escher.
<DrawingHands.jpg>
In math, for those who rememeber what are the phi_i (the partial
computable function) this is
Ee phi_e = e.
The physical implementation of the picture itself is part of the
implied meaning of this picture.
And physics has nothing to do with this.
and if resources are not available then there is no way to claim
access to the information that would be in the solution that the
computation would generate. WE might try to get around this
problem the way that Bruno does by stipulating that the "truth"
of the solution gives it existence, but the fact that some
mathematical statement or sigma_1 sentence is true (in the prior
sense) does not allow it to be considered as accessible for use
for other things. For example, we could make valid claims about
the content of a meteor that no one has examined but we cannot
have any certainty about those claims unless we actually crack
open the rock and physically examine its contents.
The state of the universe as "moving harmoniously together"
was not exactly what the PEH was for Leibniz. It was the
synchronization of the simple actions of the Monads. It was a
coordination of the percepts that make up the monads such that,
for example, my monadic percept of living in a world that you
also live in is synchronized with your monadic view of living in
a world that I also live in such that we can be said to have
this email chat. Remember, Monads (as defined in the Monadology)
have no windows and cannot be considered to either "exchange"
substances nor are embedded in a common medium that can exchange
excitations. The entire "common world of appearances" emerges
from and could be said to supervene upon the synchronization of
internal (1p subjective) Monadic actions.
I argue that the only way that God could find a solution to
the NP-Complete problem is to make the creation of the universe
simulataneous with the computations so that the universe itself
is the computer that is finding the
solution. <snip>
Even some non universal machine can solve NP-complete problem.
Yes, of course. But they cannot solve it in zero computational
steps.
?
No computation can solve an NP-Complete problem (or perform any
computation) in zero steps. A simple and often forgotten fact.
Not true. the instruction "do nothing" can be completed in zero step.
Leibniz' PEH, to be consistent with his requirement, would have to
do the impossible. I am porposing a way to solve this impossibility.
?
Do you understand Pratt's proposal? His ratmec paper http://boole.stanford.edu/pub/ratmech.pdf
was just a crude sketch of an idea... He discussed some open
problems in the Chu_k scheme, but I have some ideas of my own and
have found ideas from others that solve most of those.
1004 fallacy, or elaborate a lot.
To be sure I am still not knowing if you have a theory, and what
you mean by "solve" in this setting.
Bruno, I have a disability.
That is not a valid argument.
I cannot write up a theory in a formal way, just as a mute person
cannot speak. It takes me several hours just to write posts like
this one as I have to go over it over and over to fix typographical
and grammatical errors and I still miss many! But if people like you
and me work together we can work of the solution and thus have a
formal theory.
Sorry, but my point is that comp leads to precise already existing
formal theories, you have to study them, like it seems you study some
of them. But it is not philosophy, it is technic. You have to do the
hard work. Some technical theoretical things have to be understood and
grasped to proceed.
Honestly, I am not interested in getting credit. I simply want the
problem solved and implemented. I am motivated by the things that it
will allow, many of which will make our world a better place.
Like anything it is double edged. My goal are not practical (if that
was not clear). Theoretical artificial is negative in being most of
the time necessarily non constructive. We cannot build intelligent
machine, nor do we really want it (nor do parents really want they
child to be intelligent and autonomous, because this needs an ability
to "let it go", than few humans have). An intelligent machine is one
which will search for an intelligent user. machine's theology is not
constructive, and put in wrong hands can even be destructive. The
universal machine is more a problem in Platonia, than a solution. We
are confronted with a big Unknown, and comp can only makes it bigger.
To get comp = to get that we cannot get comp, that we can only scratch
on the surface of it, and that we are *much* more ignorant than
before, and with some hope, more modest and wiser ...
Bruno
http://iridia.ulb.ac.be/~marchal/
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